%I A045501
%S A045501 1,1,4,14,54,233,1101,5625,30846,180474,1120666,7352471,50772653,
%T A045501 367819093,2787354668,22039186530,181408823710,1551307538185,
%U A045501 13756835638385,126298933271289,1198630386463990,11742905240821910
%N A045501 Third-from-right diagonal of triangle A121207.
%C A045501 With leading 0 and offset 2: number of permutations beginning with 321 
               and avoiding 1-23. - Ralf Stephan, Apr 25 2004
%C A045501 Second diagonal in table of binomial recurrence coefficients. Related 
               to A040027. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2008
%C A045501 Equals eigensequence of triangle A104712 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Apr 10 2009]
%H A045501 S. Kitaev, <a href="http://www.mat.univie.ac.at/users/slc/public_html/
               wpapers/s48kitaev.html">Generalized pattern avoidance with additional 
               restrictions</a>, Sem. Lothar. Combinat. B48e (2003).
%H A045501 S. Kitaev and T. Mansour, <a href="http://arXiv.org/abs/math.CO/0205182">
               Simultaneous avoidance of generalized patterns</a>.
%F A045501 a(n+1) = Sum_{k=0..n} binomial(n+2, k+2)*a(k). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Nov 10 2003
%F A045501 With offset 2, e.g.f.: x^2 + exp(exp(x))/2 * int[0..x, t^2*exp(-exp(t)+t) 
               dt]. - Ralf Stephan, Apr 25 2004
%F A045501 G.f.: A(x) = Sum(x^(k+1)/((1-k*x)^2*Product(1-l*x,l=0..k)),k=0..infinity). 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2008
%Y A045501 Cf. A045499, A045500.
%Y A045501 A104712 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 10 2009]
%Y A045501 Sequence in context: A118896 A145211 A060898 this_sequence A162481 A088655 
               A149490
%Y A045501 Adjacent sequences: A045498 A045499 A045500 this_sequence A045502 A045503 
               A045504
%K A045501 easy,nonn
%O A045501 1,3
%A A045501 H. W. Gould (gould(AT)math.wvu.edu)
%E A045501 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 10 2003
%E A045501 Entry revised by N. J. A. Sloane (njas(AT)research.att.com) Dec 11 2006